The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 páginas |
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Página 28
... greater than AB . Wherefore , the greater angle , & c . Q. E. D. See N. a 3. 1 . PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater ...
... greater than AB . Wherefore , the greater angle , & c . Q. E. D. See N. a 3. 1 . PROP . XX . THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ; any two sides of it together are greater ...
Página 29
... greater than BE . To each of these add EC ; Book I. therefore the sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are great- er than CD , add DB to each of these ; therefore the sides ...
... greater than BE . To each of these add EC ; Book I. therefore the sides BA , AC are greater than BE , EC : again , because the two sides CE , ED of the triangle CED are great- er than CD , add DB to each of these ; therefore the sides ...
Página 31
... greater than the an- gle EDF ; the base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line ĎE , make a the angle EDG equal ...
... greater than the an- gle EDF ; the base BC is also greater than the base EF . Of the two sides DE , DF , let DE be the side which is not greater than the other , and at the point D , in the straight line ĎE , make a the angle EDG equal ...
Página 32
... greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equala to EF ; but it is not ; therefore the angle BAC is not equal to the angle EDF ; neither is it ...
... greater , it must either be equal to it , or less ; but the angle BAC is not equal to the angle EDF , because then the base BC would be equala to EF ; but it is not ; therefore the angle BAC is not equal to the angle EDF ; neither is it ...
Página 35
... greater ; and because the an- gle AGH is greater than the an- E A- G C. B D H F gle GHD , add to each of them the angle BGH ; therefore the angles AGH , BGH are greater than the angles BGH , GHD ; but the angles AGH , BGH are equal a to ...
... greater ; and because the an- gle AGH is greater than the an- E A- G C. B D H F gle GHD , add to each of them the angle BGH ; therefore the angles AGH , BGH are greater than the angles BGH , GHD ; but the angles AGH , BGH are equal a to ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Pasajes populares
Página 30 - Any two sides of a triangle are together greater than the third side.
Página 64 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Página 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
Página 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 165 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Página 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Página 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Página 39 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Página 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.